Average Error: 15.5 → 0.4
Time: 17.3s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r25937 = r;
        double r25938 = b;
        double r25939 = sin(r25938);
        double r25940 = r25937 * r25939;
        double r25941 = a;
        double r25942 = r25941 + r25938;
        double r25943 = cos(r25942);
        double r25944 = r25940 / r25943;
        return r25944;
}
↓
double f(double r, double a, double b) {
        double r25945 = r;
        double r25946 = a;
        double r25947 = cos(r25946);
        double r25948 = b;
        double r25949 = cos(r25948);
        double r25950 = r25947 * r25949;
        double r25951 = sin(r25948);
        double r25952 = r25950 / r25951;
        double r25953 = sin(r25946);
        double r25954 = r25952 - r25953;
        double r25955 = r25945 / r25954;
        return r25955;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.5

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied associate-/l*0.4

    \[\leadsto \color{blue}{\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}}\]

  6. Simplified0.4

    \[\leadsto \frac{r}{\color{blue}{\frac{\cos a \cdot \cos b}{\sin b} - \frac{\sin a}{1}}}\]

  7. Taylor expanded around inf 0.4

    \[\leadsto \color{blue}{\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}}\]

  8. Simplified0.4

    \[\leadsto \color{blue}{\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}}\]

  9. Final simplification0.4

    \[\leadsto \frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\]

Reproduce

herbie shell --seed 2019209 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))